Storage and Handling:
Basil is a warm weather crop that is sensitive to cold temperatures which is why it will turn black if you put it in the fridge.
To keep basil, strip off a few of the bottom leaves, trim the stems and set in a cup or small vase with water and keep on your kitchen counter. Now take the stripped leaves (or all of your basil if your bunch has really short stems) and wrap them in a dry paper towel (wet leaves will quickly turn black) and store in an airtight container at 50 degrees or room temperature.
(Storage tips courtesy Farmer John’s Cookbook, The Real Dirt on Vegetables)